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    <h1 >M.Sc. & Ph.D. Defences</h1>
		<div class="page-title-hline">&nbsp;</div>








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<table cellpadding="3" cellspacing="2">
  <tr>
    <td colspan="2"><p style="; font-weight: bold;">Upcoming Defence </p></td>
  </tr>
  <tr>
    <td>Title:</td>
    <td> Analysis of the  Dynamic Traveling Salesman Problem with Different Policies </td>
  </tr>
  <tr>
    <td>Speaker:</td>
    <td><span style="margin-top: 0; margin-bottom: 0;">Mr. Santiago Ravassi (M.Sc.) </span></td>
  </tr>
  <tr>
    <td width="54">Date:</td>
    <td><span style="margin-top:0;margin-bottom:0;">Thursday, December 8 , 2011 </span></td>
  </tr>
  <tr>
    <td>Time:</td>
    <td><span style="margin-top:0;margin-bottom:0;">1:30 p.m. </span></td>
  </tr>
  <tr>
    <td>Location:</td>
    <td><span style="margin-top:0;margin-bottom:0;">LB 921-4      (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</span></td>
  </tr>
  <tr>
    <td>Abstract:</td>
    <td><p style="text-align:justify;margin-top:0;margin-bottom:0;">We propose and analyze new policies for the  traveling salesman problem in a dynamic and stochastic environment (DTSP). The  DTSP is defined as follows: demands for service arrive in time according to a  Poisson process, are independent and uniformly distributed in a Euclidean  region of bounded area, and the time service is zero; the objective is to  reduce the time the server visits all the present demands for the first time.  We start by analyzing the nearest neighbour (NN) policy since it has the best  performance for the dynamic vehicle routing problem (DTRP), a closely related  problem to the DTSP. We further introduce the random start policy whose  efficiency is similar to that of NN, and we observe that when the random start  policy is delayed, it behaves as the DTRP with NN policy. Finally, we introduce  the partitioning policy and show that it reduces the expected time demands are  swept from the region for the first time relative to other policies</p></td>
  </tr>
</table>
<table cellpadding="3" cellspacing="2">
  <tr>
    <td colspan="2"><p style="; font-weight: bold;">Past Defences </p></td>
  </tr>
  <tr>
    <td>Title:</td>
    <td><span style="margin-top:0;margin-bottom:0;">On Existence and Stability of Absolutely Continuous Invariant Measures in Some Chaotic Dynamical Systems </span></td>
  </tr>
  <tr>
    <td>Speaker:</td>
    <td><span style="margin-top: 0; margin-bottom: 0;">Mr. Peyman Eslami (Ph.D.)</span></td>
  </tr>
  <tr>
    <td width="54">Date:</td>
    <td><span style="margin-top:0;margin-bottom:0;">Friday, September 9, 2011 </span></td>
  </tr>
  <tr>
    <td>Time:</td>
    <td><span style="margin-top:0;margin-bottom:0;">10:30 a.m. </span></td>
  </tr>
  <tr>
    <td>Location:</td>
    <td><span style="margin-top:0;margin-bottom:0;">LB 921-4      (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</span></td>
  </tr>
  <tr>
    <td>Abstract:</td>
    <td><span style="margin-top:0; margin-bottom: 0;">(Click <a href="http://cuma1.mathstat.concordia.ca/documents/EslamiPAbstract.pdf">here</a> to view)</span></td>
  </tr>
</table>
<table cellpadding="3" cellspacing="2">
  <tr>
    <td>Title:</td>
    <td><span style="margin-top:0;margin-bottom:0;">APOS Theory as a Framework to Study the Conceptual Stages of Related Rates Problems </span></td>
  </tr>
  <tr>
    <td>Speaker:</td>
    <td><span style="margin-top: 0; margin-bottom: 0;">Mr. Mathew Tziritas (M.T.M)</span></td>
  </tr>
  <tr>
    <td width="54">Date:</td>
    <td><span style="margin-top:0;margin-bottom:0;">Wednesday, September 7, 2011 </span></td>
  </tr>
  <tr>
    <td>Time:</td>
    <td><span style="margin-top:0;margin-bottom:0;">10:00 a.m. </span></td>
  </tr>
  <tr>
    <td>Location:</td>
    <td><span style="margin-top:0;margin-bottom:0;">LB 921-4      (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</span></td>
  </tr>
  <tr>
    <td>Abstract:</td>
    <td><p style="margin-top:0;margin-bottom:0;">A study was done in an attempt to use the APOS  theory of learning and teaching mathematics to develop and test a teaching  cycle for the improvement of students&rsquo; conceptual understanding of related  rates problems. &ldquo;APOS&rdquo; is an acronym that stands for Action, Process, Object,  and Schema, and refers to both a theory of teaching and learning and a research  methodology in mathematics education. APOS theory originated in the research of  an American mathematician and mathematics educator Ed Dubinsky on undergraduate  students&rsquo; learning of mathematics (Calculus, Linear Algebra, Abstract Algebra).  &ldquo;Related rates problems&rdquo;  refers to problems in Calculus that require finding the rate of change of one  value, given the rate of change of a related value.</p>
      <p style="text-align:justify; margin-top:0;">Part of APOS research methodology is a &ldquo;genetic  decomposition&rdquo; of the concepts to be learned by the students in terms of the  mental constructions that such learning requires. In the present study, the  genetic decomposition focused on the mental constructions required for student  success during the initial conceptual stages of related rates problems  learning. The decomposition was constructed using the author&rsquo;s knowledge of the  subject. The genetic decomposition was used to construct an Action &ndash; Discussion  &ndash; Exercise (ACE) teaching cycle which was then tested on two groups of  students. Finally, students were asked to solve related rates problems during  an individual interview with the author. Data from students&rsquo; involvement in the  ACE cycle as well as their work during the interview process were then used to  suggest changes to the genetic decomposition and the ACE cycle. These  suggestions constitute the results of the study. Their purpose is to improve  the starting point for further iterations of experimentation of teaching related  rates problems. </p>
      <span style="margin-top:0; margin-bottom: 0;"><a href="http://cuma1.mathstat.concordia.ca/documents/EslamiPAbstract.pdf"></a></span></td>
  </tr>
</table>
<table cellpadding="3" cellspacing="2">
  <tr>
    <td>Title:</td>
    <td><span style="margin-top:0;margin-bottom:0;">Parameter Estimation in a Two-Dimensional Commodity </span></td>
  </tr>
  <tr>
    <td>Speaker:</td>
    <td><span style="margin-top: 0; margin-bottom: 0;">Ms. Wenxi Liu (M.Sc.)</span></td>
  </tr>
  <tr>
    <td width="54">Date:</td>
    <td><span style="margin-top:0;margin-bottom:0;">Wednesday, August 31, 2011 </span></td>
  </tr>
  <tr>
    <td>Time:</td>
    <td><span style="margin-top:0;margin-bottom:0;">2:00 p.m. </span></td>
  </tr>
  <tr>
    <td>Location:</td>
    <td><span style="margin-top:0;margin-bottom:0;">LB 921-4      (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</span></td>
  </tr>
  <tr>
    <td>Abstract:</td>
    <td><span style="margin-top:0; margin-bottom: 0;">We consider the problem of  estimating the parameters of an unobservable model for the spot price of a  commodity. Using the observable time-series of the term-structure of futures  prices and a filter-based implementation of the expectation maximization (EM)  algorithm, we calculate the maximum likelihood parameter estimates (MLEs). New  finite-dimensional filters are derived that allow the EM algorithm to be  implemented without calculating Kalman smoother estimates. The method is  applied to a two-factor commodity price model.</span></td>
  </tr>
</table>
<table cellpadding="3" cellspacing="2">
  <tr>
    <td>Title:</td>
    <td><span style="margin-top:0;margin-bottom:0;">Theory and Applications of Generalized Linear Models in Insurance </span></td>
  </tr>
  <tr>
    <td>Speaker:</td>
    <td><span style="margin-top: 0; margin-bottom: 0;">Mr. Jun Zhou (Ph.D.)</span></td>
  </tr>
  <tr>
    <td width="54">Date:</td>
    <td><span style="margin-top:0;margin-bottom:0;">Monday, August 29, 2011 </span></td>
  </tr>
  <tr>
    <td>Time:</td>
    <td><span style="margin-top:0;margin-bottom:0;">10:00 a.m. </span></td>
  </tr>
  <tr>
    <td>Location:</td>
    <td><span style="margin-top:0;margin-bottom:0;">LB 921-4      (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</span></td>
  </tr>
  <tr>
    <td>Abstract:</td>
    <td><span style="margin-top:0;margin-bottom:0;">(Click <a href="http://cuma1.mathstat.concordia.ca/documents/JunZhouAbstract.pdf">here</a> to view)</span></td>
  </tr>
</table>
<p style="margin-bottom: 0;">&nbsp;</p>
<p style="margin-top:0;margin-bottom:0;"><strong><a href="http://cuma1.mathstat.concordia.ca/EventsNewsDefences.html#top"></a></strong>&nbsp; </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Speaker: </strong>Mr. Oscar Quijano Xacur (M.Sc.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date: </strong>Tuesday, August 23, 2011 </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 1:30 p.m. </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> LB 921-4      (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title: </strong> Property and Casualty Premiums Based on Tweedie Families of Generalized Linear Models </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Abstract: </strong>We consider the problem of estimating  accurately the pure premium of a property and casualty insurance portfolio when  the individual aggregate losses can be assumed to follow a compound Poisson  distribution with gamma jump size. The Generalized Linear Models (GLMs) with a  Tweedie response distribution are analyzed as a method for this estimation.  This approach is compared against the standard practice in the industry of  combining estimations obtained separately for the frequency and severity by  using GLMs with Poisson and gamma responses respectively. We show that one  important difference between these two methods is the variation of the scale  parameter of the compound Poisson-gamma distribution when it is parametrized as  an exponential dispersion model. We conclude that both approaches need to be  considered during the process of model selection for the pure premium.</p>
<p style="margin-top:0;margin-bottom:0;"><a href="http://cuma1.mathstat.concordia.ca/documents/RaminOkhratiAbstract.pdf"></a></p>
<p style="margin-top:0;margin-bottom:0;"><strong>Speaker: </strong>Mr. Petr Zorin (M.Sc.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date: </strong>Tuesday, August 23, 2011</p>
<p style="margin-top:0; margin-bottom: 0;"><strong>Time:</strong> 11:00 a.m. </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> LB 921-4      (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title: </strong> The Discrete Spectra of Dirac Operators </p>
<p style="margin-top:0;"><strong>Abstract: </strong>A single particle is bound by an attractive  central potential and obeys the Dirac equation in d dimensions.   The Coulomb potential is one of the few  examples for which exact analytical solutions are available. A geometrical  approach called 'the potential envelope method' is used to study the discrete  spectra generated by potentials V(r) that are smooth transformations V(r) =  g(-1/r)  of the soluble Coulomb  potential.  When g has definite  convexity, the method leads to energy bounds. This is possible because of the  recent comparison theorems for the Dirac equation. The results are applied to  study soft-core Coulomb potentials used as models for confined atoms. The  estimates are compared with accurate eigen values found by numerical methods.</p>
<p style="margin-bottom: 0;"><strong>Speaker: </strong>Ms. Anne Mackay (M.Sc.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date: </strong>Monday, August 22, 2011 </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 1:00 p.m. </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> LB 921-4      (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title: </strong> Pricing and Hedging Equity-Linked Products Under Stochastic Volatility Models </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Abstract: </strong>Equity-indexed annuities (EIAs) are becoming increasingly interesting  for investors as market volatility increases. Simultaneously, they represent a  higher risk for insurers, which amplifies the need for hedging strategies that  perform well when index returns present unexpected changes in their volatility.  In this thesis, we introduce hedging strategies that aim at reducing the risk  of the financial guarantees embedded in EIAs.</p>
<p style="text-align:justify;margin-top:0;margin-bottom:0;"> We first derive closed-form expressions for the price and the Greeks of  a point-to-point EIA under the Heston model, which assumes stochastic  volatility. To do so, we rely on the similarity between the payoff of a  European call option and that of the EIA. We use the Greeks to develop dynamic  hedging strategies that aim at reducing equity and volatility risk. Using Monte  Carlo simulations to derive the distribution of the resulting hedging errors,  we compare the performance of hedging strategies that use the Greeks derived  under the Heston model to other strategies based on Greeks developed under  Black-Scholes.</p>
<p style="text-align:justify;margin-top:0;margin-bottom:0;"> We show that, when the market is Hestonian, the performance of hedging  strategies developed in a Black-Scholes framework are significantly affected by  the calibration of the model and the volatility risk premium. We further show  that the performance of a simple delta hedging strategy using Heston Greeks is  also reduced by the presence of a volatility risk premium, and that this  performance can be improved by incorporating gamma or vega hedging to the  strategy. We conclude by recommending the use of a delta-vega hedging strategy  to reduce model calibration and volatility risk.</p>
<p style="margin-top:0;margin-bottom:0;"><strong><a href="http://cuma1.mathstat.concordia.ca/EventsNewsDefences.html#top"></a></strong></p>
<p style="margin-top:0;margin-bottom:0;"><strong>Speaker: </strong>Ms. Mengjue Tang (M.Sc.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date: </strong>Tuesday, July 26, 2011 </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 10:30 a.m. </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> LB 921-4      (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title:</strong> A Comparison of Two Nonparametric Density  Estimators in the Context of Actuarial Loss Model </p>
<p align="justify" style="margin-top:0;"><strong>Abstract:</strong>  In  this thesis, I will introduce two estimation methods for estimating loss  function in actuarial science. Both of them are related to nonparametric  density estimation (kernel smoothing). One is deriving from kernel smoothing  which is called semi-parametric transformation kernel smoothing while another  one derives from Hille's lemma and perturbation idea which is quite similar to  kernel smoothing. As the increasing frequently used of nonparametric density  estimation in many areas, actuaries are more likely to use this kind of simple  method when doing decision-making. There are now existing many nonparametric  density estimation methods, but which one is better? In order to compare the  two methods which are introduced in this thesis, I conduct simulation study on  both of them and try to find out which one is preferable and easier to apply.  Also the second method which derives from Hille's lemma gives us a new idea  about how to estimate loss function when we are doing decision-making in  actuarial science.</p>
<p style="margin-bottom: 0;"><strong>Speaker: </strong>Mr. Ramin Okhrati (Ph.D.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date: </strong>Monday, July 25, 2011 </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 10:00 a.m. </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> LB 921-4      (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title: </strong> Credit Risk Modeling under Jump Processes and under a Risk Measure-Based Approach </p>
<p style="margin-top:0;"><strong>Abstract: </strong> <a href="http://cuma1.mathstat.concordia.ca/documents/RaminOkhratiAbstract.pdf">(Click here to view)</a> </p>
<p style="margin-bottom: 0;"><strong>Speaker: </strong>Ms. Li Ma (Ph.D.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date: </strong>Monday, June 27, 2011 </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 2:00 p.m. </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> LB 921-4      (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title: </strong> Generalized Feynman-Kac Transformation and Fukushima's Decomposition for Nearly Symmetric Markov Processes </p>
<p style="margin-top:0;"><strong>Abstract: </strong> <a href="http://cuma1.mathstat.concordia.ca/documents/LiMaAbstract.pdf">(Click here to view)</a></p>
<p style="margin-bottom: 0;"><strong>Speaker: </strong>Ms. Yasmine Raad (M.Sc.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date: </strong>Wednesday, June 22, 2011 </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 10:00 a.m. </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> LB 921-4      (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title:</strong> Comparison theorems  for the principal eigenvalue of the Laplacian </p>
<p align="justify" style="margin-top:0;"><strong>Abstract:</strong> We study the Faber -  Krahn inequality for the Dirichlet eigenvalue problem of the Laplacian, first  in $\mathbb{R}^N$, then on a compact smooth Riemannian manifold $M$. For the  latter, we consider two cases. In the first case, the compact manifold has a  lower bound on the Ricci curvature, in the second, the integral of the  reciprocal of an isoperimetric estimator function of the Riemannian manifold is  convergent. In all cases, we show that the first eigenvalue of a domain in  $\mathbb{R}^N$, respectively $M$, is minimal for the ball of the same volume,  respectively, for a geodesic ball of the same relative volume in an appropriate  manifold $M^\ast$. While working with the isoperimetric estimator, the manifold  $M^\ast$ need not have constant sectional curvature. In $\mathbb{R}^N$, we also  consider the Neumann eigenvalue problem and present the Szeg\"o -  Weinberger inequality. In this case, the principal eigenvalue of the ball is  maximal among all principal eigenvalues of domains with same volume.<br />
</p>
<p style="margin-bottom: 0;"><strong>Speaker: </strong>Mr. Alexandre Laurin (M.Sc.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date: </strong>Friday, April 1, 2011 </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 1:30 p.m. </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> LB 921-4      (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title:</strong> On Duncan's characterization of McKay's monstrous E_8 </p>
<p align="justify" style="margin-top:0;"><strong>Abstract:</strong> McKay's Monstrous $E_8$ observation has  provided further evidence, along with the evidence provided by the study of  Monstrous Moonshine, that the Monster is intimately linked with a wide spectrum  of other mathematical objects and, one might even say, with the natural  organization of the universe. Although these links have been observed and facts  about them proved, we have yet to understand exactly where and how they  originate. We here review a set of conditions, due to Duncan, imposed on  arithmetic subgroups of $PSL2(R)$ that return McKay's Monstrous $E_8$ diagram.  The purpose is to compare these with Conway, McKay and Sebbar's (CMS)  conditions that return the complete set of Monstrous Moonshine groups in order  to gain some insight on their meaning. By way of doing this review of Duncan's  conditions, we will also review and elaborate on Conway's method for  understanding groups like $\Gamma_0(N)$.</p>
<p style="margin-bottom: 0;"><strong>Speaker: </strong>Mr. Jun Li (Ph.D.) </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date: </strong>Monday, November 29, 2010 </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 1:30 p.m. </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> H  762     (Concordia University, Hall Building, 1455 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title:</strong> Some Contributions to Nonparametric Estimation of Density and Related Functionals for Biased Data</p>
<p align="justify" style="margin-top:0;"><strong>Abstract:</strong>  Length biased sampling as a special case of biased sampling occurs  naturally in many statistical applications. One aspect regarding length biased  data in which people are interested is estimating the underlying true density  with the observed samples. Since most length biased data are nonnegative, the  true density has a support with a non-negative finite end point. The current  proposed kernel density estimators with symmetric kernels may have large bias  at the lower boundary. In this thesis, we propose some new smooth density  estimators with weights generating from Poisson distribution or nonnegative  asymmetric kernels for length biased data to take care of the edge effect. Besides  density estimators, we also consider smooth estimators of distribution function  and functions related to distribution and density function, such as hazard  function and mean residual life function. Our methods are easily to extend to  the general biased data as well.</p>
<p style="margin-bottom: 0;"><strong>Speaker: </strong>Ms. Di Xu (M.Sc.) </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date: </strong>Friday, November 26, 2010 </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 10:00 a.m. </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> LB 921-4 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title:</strong> The Range Time for Jump Diffusion with Two-Sided Exponential Jumps</p>
<p align="justify" style="margin-top:0;"><strong>Abstract:</strong> The  range time for a stochastic process is the stopping time when the difference  between its running maximum and running minimum first exceeds a certain level.  It has been studied by several authors for random walks and diffusion  processes. In this presentation we consider a jump diffusion process with  two-sided exponential jumps. By a martingale approach, we first solve the  two-sided exit problem for this jump diffusion process. Using solutions to the  exit problem, we then obtain several results concerning the range time related  to joint distributions for the jump diffusion. </p>
<p style="margin-bottom: 0;"><strong>Speaker: </strong>Ms. Janine Bachrachas (M.Sc.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date: </strong>Monday, November 22, 2010 </p>
<p style="margin-top:0;margin-bottom:0;"><a href="../../../../pageswww.concordia.ca/index.html">\</a><strong>Time:</strong> 1:30 p.m. </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> LB 921-4    (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title:</strong> On the Mean Curvature Flow </p>
<p align="justify" style="margin-top:0;"><strong>Abstract:</strong> We present a self-contained expository review on the mean  curvature flow for smooth embedded hypersurfaces in the (n+1)-dimensional  Euclidean space. We start by addressing the short time existence of solutions  to the flow, followed by the long time existence in the case of compact convex  hypersurfaces and entire graphs. Although the results presented here are part  of the classical literature originated in the 80&rsquo;s, we derive all necessary  calculations and gather the simplest possible approach in view of later  developments of the area.</p>
<p style="margin-bottom: 0;"><strong>Speaker: </strong>Ms. Yafang Wang (Ph.D.) </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date: </strong>Friday, October 29, 2010 </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 3:30 p .m.</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> LB 921-4 (Concordia University, Hall Building, 1400 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title:</strong> The Distribution of the Discounted Compound PH-Renewal Process </p>
<p align="justify" style="margin-top:0;"><strong>Abstract:</strong> The family of phase--type (PH) distributions has many  useful properties such as closure under convolution and mixtures, as well as  rational Laplace transforms. PH distributions  are widely used in applications of stochastic models such as in queuing  systems, biostatics and engineering. They are also applied to insurance risk,  such as in ruin theory.&nbsp; In this thesis, we extend the work of Wang (2007),  that discussed the moment generating function (mgf) of discounted compound sums  with PH inter--arrival times under a nonzero net interest rate. Here we focus  on the distribution of the discounted compound sums. This represents a  generalization of the classical risk model for which the net interest rate is  zero.&nbsp; A differential equation system  is derived for the mgf of a discounted compound sum with PH inter--arrival  times and any claim severity if its mgf exists. For some PH inter-arrival times,  we can further simplify this differential equation system. If the matrix is  order of 2, an ordinary differential equation is developed for PH inter-arrival  times. By inverting the corresponding Laplace  transforms, the density functions and cumulative distribution functions are  also obtained. In addition, the series and transformation methods for solving  differential equations are discussed, when the mean of inter-arrival times is  small.&nbsp; Applications such as stop-loss premiums, and risk measures  such as VaR and CTE are investigated. These are compared for different  inter-arrival times.  Some numerical  examples are given to illustrate the results.&nbsp; Finally asymptotic results have been discussed, when  the mean inter-arrival time goes to zero. We obtain normality to approximate  compound renewal processes. The asymptotic normal distribution is also derived  for the discounted compound renewal sum at a fixed time.</p>
<p style="margin-bottom: 0;"><strong>Speaker: </strong>Mr. Xinghua Zhou (M.Sc.) </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date: </strong>Thursday, September 2,  2010 </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 10:00 a.m.</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> LB 921-4  (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title:</strong> Stochastic Flow and FBSDE Approaches to Quadratic  Term  Structure Models </p>
<p align="justify" style="margin-top:0;"><strong>Abstract:</strong> We  study the stochastic flow method and Forward-Backward Stochastic Differential  Equation (FBSDE) approach to Quadratic Term Structure Models (QTSMs).  Applying the stochastic flow approach, we get  a closed form solution for the zero-coupon bond price under a one-dimensional  QTSM.  However, in the higher dimensional  cases, the stochastic flow approach is difficult to implement. Therefore, we  solve the n-dimensional QTSMs by implementing the FBSDE approach, which shows  that the zero-coupon bond price under QTSM provided some Riccati type equations  have global solutions. </p>
<p style="margin-bottom: 0;"><strong>Speaker: </strong>Ms. Wenxia Li (M.Sc.) </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date:</strong> Friday, August 27, 2010 </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 10:30 a.m.</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> LB 921-4  (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title:</strong> Optimal Surrender and Asset Allocation Strategies for Equity-Indexed  Insurance Investors </p>
<p align="justify" style="margin-top:0;"><strong>Abstract:</strong> Equity-indexed annuity (EIA)  products is getting more and more popular since first introduced in 1995. An  EIA investor may consider surrendering the contract before maturity and invest  in the stock index in order to earn the full stock growth. We consider an  EIA policyholder who seeks the optimal surrender strategy and asset allocation  strategy after surrender in order to maximize his expected discounted utility  at the maturity of the contract or his time of death, whichever comes first.  The optimal value functions satisfy Hamilton-Jacobi-Bellman equations from  which the optimal strategies are derived. </p>
<p style="margin-bottom: 0;"><strong>Speaker:</strong> Mr. Ferenc Balogh  (Ph.D.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date:</strong> Tuesday, July 20, 2010</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 11:00 a.m.</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> H 443 (Concordia University, Hall Building, 1455 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title:</strong> Orthogonal Polynomials, Equilibrium Measures and Quadrature Domains Associated with Random Matrix Models </p>
<p align="justify" style="margin-top:0;"><strong>Abstract:</strong> Motivated by asymptotic questions related to the spectral theory of complex random matrices, this work focuses on the asymptotic analysis of orthogonal polynomials with respect to quasi-harmonic potentials in the complex plane. The ultimate goal is to develop new techniques to obtain strong asymptotics (asymptotic expansions valid uniformly on compact<br />
  subsets) for planar orthogonal polynomials and use these results to understand the limiting behavior of spectral statistics of matrix models as their size goes to infinity. For orthogonal polynomials on the real line the powerful Riemann--Hilbert approach is the main analytic tool to derive asymptotics for the eigenvalue correlations in Hermitian matrix models. As yet, no such method is available to obtain asymptotic information about planar orthogonal polynomials, but some steps in this direction have been taken.&nbsp; The results of this thesis concern the connection between the asymptotic behavior of orthogonal polynomials and the corresponding equilibrium measure. It is conjectured that this connection is established via a quadrature identity: under certain conditions the weak-star limit of the normalized zero counting measure of the orthogonal polynomials is a quadrature measure for the support of the equilibrium measure of the corresponding two-dimensional electrostatic variational problem of the underlying potential.&nbsp; Several results are presented on equilibrium measures, quadrature domains, orthogonal polynomials and their relation to matrix models. In particular, complete strong asymptotics are obtained for the simplest nontrivial quasi-harmonic potential by a contour integral reduction method and the Riemann-Hilbert approach, which confirms the above conjecture for this special case.</p>
<p style="margin-bottom: 0;"><strong>Speaker:</strong> Mr. Farhat Abohalfya  (Ph.D.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date:</strong> Tuesday, May 11, 2010</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 1:00 p.m.</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> H 443 (Concordia University, Hall Building, 1455 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title:</strong> On RG-spaces and the Space of Prime d-ideals in C(X)</p>
<p align="justify" style="margin-top:0;margin-bottom:0;"><strong>Abstract:</strong> Let A be a commutative semiprime ring with identity. Then A has at least two epimorphic regular extensions namely, the universal epimorphic regular extension T(A), and the epimorphic hull H(A). We are mainly interested in the case of C(X), the ring of real-valued continuous functions defined on a Tychonoff space X. It is a commutative semiprime ring with identity and it has another important epimorphic regular extension namely, the minimal regular extension G(X). In our study we show in chapter 5 that the spectrum of the ring H(A) with the spectral topology is homeomorphic to the space of the prime &xi;-ideals in A with the patch topology. In the case of C(X), the spectrum of the epimorphic hull H(X) with the spectral topology is homeomorphic to the space of prime d-ideals in C(X) with the patch topology.</p>
<p style="text-align:justify;margin-top:0;margin-bottom:0;">A Tychonoff space X  which satisfies the property that G(X) = C(X&delta;) is called an RG-space. We shall introduce a new class of topological spaces namely the class of almost k-Baire spaces, and as a special case of this class we shall have the class of almost Baire spaces. We show that every RG-space is an almost Baire space but it need not be a Baire space. However, in the case of RG-spaces of countable pseudocharacter, RG-spaces have to be Baire spaces. Furthermore, in this case every dense set in RG-spaces has a dense interior.</p>
<p style="text-align:justify; margin-top:0;">The Krull z-dimension and the Krull d-dimension will play an important role to determine which of the extensions H(X) and G(X) has the form of a ring of real-valued continuous functions on some topological space. In [31] the authors gave some techniques to prove that there is no RG-space with infinite Krull z-dimension, but there was an error that we found in the proof of theorem 3.4. In this study, we will give an accurate proof which applies to many spaces but the general theorem will remain open. And we will use the same techniques to prove that if C(X) has an infinite chain of prime d-ideals then H(X) cannot be isomorphic to a ring of real-valued continuous functions.</p>
<p style="margin-bottom: 0;"><span style="font-weight: bold">Speaker:</span> Ms. Noushin Sabetghadam Haghighi (Ph.D.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date:</strong> Thursday, April 8, 2010</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time: </strong>3:00 p.m.</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room:</strong> LB 649 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) </p>
<p style="margin-top:0;margin-bottom:0;"><span style="font-weight: bold">Title:</span> On Larcher Subgroups and Fourier Coefficients of Modular Forms</p>
<p align="justify" style="margin-top:0;"><strong><strong>Abstract: </strong></strong>This work consists of two parts, both revolving around Monstrous moonshine. First we compute the signature of Generalized Larcher subgroups.   These subgroups were first introduced by Larcher to prove his result about the cusp widths of any congruence subgroup. They also played a significant role in the classification of torsion-free low genus congruence subgroups. In the second part, we establish universal recurrence formulae satisfied by the Fourier coefficients of meromorphic modular forms on moonshine-type subgroups. </p>
<p style="margin-bottom: 0;"><span style="font-weight: bold">Speaker:</span> Ms. Huan Yi Li (M.Sc.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date:</strong> Wednesday, April 7 , 2010</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 10:30 a.m.</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room</strong>: LB 921-4 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title:</strong> Analyzing Equity-Indexed Annuities Using Lee-Carter Stochastic Mortality Model </p>
<p align="justify" style="margin-top:0;"><strong>Abstract:</strong> Equity-indexed annuity (EIA) insurance products have become more and more popular since being introduced in 1995. Some of the most important characteristics of these products are that they allow the policyholders to benefit from the equity market&rsquo;s potential growth and ensure that the principals can grow with a minimum guaranteed interest rate. In this thesis, we show how to derive the closed-form pricing formula of a point-to-point (PTP) financial guarantee, using the Black-Scholes framework. Furthermore, the PTP equity-indexed annuity is discussed in details as well. We will show how to construct the replicating portfolio for both the PTP financial guarantee and the PTP equity-indexed annuity. Because in the real financial market, companies cannot trade continuously, which violates the assumptions of the complete-market, the replicating portfolio will generate hedging errors. The distributions of the present values hedging errors for both the financial guarantee and EIA will be shown. In addition, the distribution of the present values of hedging errors will be showed. We will talk about the impacts on the hedging errors caused by the stochastic mortality rates in the end of the thesis. </p>
<p style="margin-bottom: 0;">Speaker: Mr. Colin Grabowski (M.Sc.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date:</strong> Wednesday, March 31 , 2010</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 11:00 a.m.</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room</strong>: LB 921-4 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title:</strong> Local Torsion on Elliptic Curves </p>
<p align="justify" style="margin-top:0;margin-bottom:0;"><strong>Abstract: </strong> Let E be an elliptic curve over Q. Let p be a prime of good reduction for E. We say that p is a local torsion prime if E has p-torsion over Qp, and more generally, we say that p is a local torsion prime of degree d if E has p-torsion over an extension of degree d of Qp. </p>
<p align="justify" style="margin-top:0;">We study in this thesis local torsion primes by presenting numerical evidence, and by computing estimates for the number of local torsion primes on aver- age over all elliptic curves over Q.</p>
<p style="margin-bottom: 0;"><span style="font-weight: bold">Speaker:</span> Mr. Amir Reza Raji-Kermany (Ph.D.)</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Date:</strong> Thursday, February 4, 2010</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Time:</strong> 10:00 a.m.</p>
<p style="margin-top:0;margin-bottom:0;"><strong>Room</strong>: LB 921-4 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) </p>
<p style="margin-top:0;margin-bottom:0;"><strong>Title:</strong> Mathematical Models for Interactions Among Evolutionary Forces in Finite and Infinite Populations</p>
<p align="justify" style="margin-top:0;"><strong>Abstract:</strong> Mathematical modeling in population genetics plays an important role in understanding the effects of different evolutionary forces on the evolution of populations. The complexity of these models increases as we include more factors affecting the genetic composition of the population under consideration.  In this thesis, we focus on interactions among evolutionary forces in finite and infinite populations. In the first part of the thesis we study the effect of migration between two populations of equal sizes with mutations occurring between two alleles at the locus under study.<br />
  Stochastic changes in the frequencies of one of the alleles in the population is described by a two-dimensional diffusion process. The stationary distribution of this process is characterized by identifying the joint moments under the stationary measure. The second part of this thesis is devoted to studying the effect of recombination on the distribution of types in an infinite haploid population with selection and mutation. In particular, we study the frequency of an allele promoting recombination in such a population. The dynamics of this system are studied in a deterministic framework where the distribution of types is described by a system of ordinary differential equations. We provide numerical solutions to this system. Our results suggest that even if there is no epistatic interaction among loci under selection, an increased rate of deleterious mutations provides a sufficient condition for recombination to be favored in the population.<em><br />
  </em></p>
<p style="margin-bottom: 0;"><span style="font-weight: bold">Speaker:</span> Mr. Zhaoyang Wu  (M.Sc.)</p>
<p style="margin-top:0;margin-bottom:0;">Date: Monday, January 25, 2010</p>
<p style="margin-top:0;margin-bottom:0;">Time: 11:00 a.m.</p>
<p style="margin-top:0;margin-bottom:0;">Room: LB 921-4 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) </p>
<p style="margin-top:0;margin-bottom:0;">Title: Predicting Stock Index Based on Grey Theory, Arima Model and Wavelet Methods</p>
<p style="text-align:justify; margin-top:0;">Abstract:   In this thesis, we develop a new forecasting method by merging traditional statistical methods with innovational non-statistical theories for the purpose of improving prediction accuracy of stock time series. The method is based on a novel hybrid model which combines the grey model, the ARIMA model and wavelet methods. First of all, we improve the traditional GM (1, 1) model to the GM (1, 1, u, v) model by introducing two parameters: the grey coefficient u and the grey dimension degree v. Then we revise the normal G-ARMA model by merging the ARMA model with the GM (1, 1, u, v) model. In order to overcome the drawback of directly modeling original stock time series, we introduce wavelet methods into the revised-ARMA model and name this new hybrid model WG-ARMA model. Finally, we obtain the WPG-ARMA model by replacing the wavelet transform with the wavelet packets decomposition. To keep consistency, all the proposed models are merged into a single model by estimating parameters simultaneously based on the total absolute error (TAE) criterion. To verify prediction performance of the models, we present case studies for the models based on the leading Canadian stock index: S&amp;P/TSX Composite Index on the daily bases. The experimental results give the rank of predictive ability in terms of the TAE, MPAE and DIR metrics as following :WPG-ARMA,WG-ARMA,G-ARMA,GM(1,1,u,v),ARIMA.</p>
<p style="margin-bottom: 0;">Speaker: Mr. Radu Gaba (Ph.D.) </p>
<p style="margin-top:0;margin-bottom:0;">Date: Tuesday, September 15, 2009</p>
<p style="margin-top:0;margin-bottom:0;">Time: 11:00 a.m.</p>
<p style="margin-top:0;margin-bottom:0;">Room: H 769 (Concordia University, Hall Building, 1455 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;">Title: On Fontaine Sheaves</p>
<p style="text-align:justify; margin-top:0;">Abstract:  In this thesis we focus our research on constructing two new types of Fontaine sheaves, Armax and Amax in the third chapter and the fourth one respectively and in proving some of their main properties, most important the localization over small affines. This pair of new sheaves plays a crucial role in generalizing a comparison isomorphism theorem of Faltings for the ramified case.  In the first chapter we introduce the concept of p-adic Galois representation and provide and analyze some examples.  The second chapter is an overview of the Fontaine Theory. We define the concept of semi-linear representation and study the period rings introduced by Fontaine while understanding their importance in classifying the p-adic Galois representations. </p>
<p style="margin-bottom: 0;">Speaker: Ms. Klara Kelecsenyi  (Ph.D.) </p>
<p style="margin-top:0;margin-bottom:0;">Date: Thursday, September 3, 2009</p>
<p style="margin-top:0;margin-bottom:0;">Time: 2:00 p.m.</p>
<p style="margin-top:0;margin-bottom:0;">Room: H 760 (Concordia University, Hall Building, 1455 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;">Title: Popularization of Mathematics as Intercultural Communication &ndash; An Exploratory Study</p>
<p style="text-align:justify;margin-top:0;margin-bottom:0;">Abstract:   Popularization of mathematics seems to have gained importance in the past decades. Besides the increasing number of popular books and lectures, there are national and international initiatives, usually supported by mathematical societies, to popularize mathematics. Despite this apparent attention towards it, studying popularization has not become an object of research; little is known about how popularizers choose the mathematical content of popularization, what means they use to communicate it, and how their audiences interpret popularized mathematics.  This thesis presents a framework for studying popularization of mathematics and intends to investigate various questions related to the phenomenon, such as:</p>
<p style="margin-top:0;margin-bottom:0;">- What are the institutional characteristics of popularization?<br />
  - What are the characteristics of the mathematical content chosen to be popularized?<br />
  - What are the means used by popularizers to communicate mathematical ideas?<br />
  - Who are popularizers and what do they think about popularization?<br />
  - Who are audience members of a popularization event?<br />
  - How audience members interpret popularization?</p>
<p style="margin-top:0;"><br />
  The thesis presents methodological challenges of studying popularization and suggests some ideas on the methods that might be appropriate for further studies. Thus it intends to offer a first step for developing suitable means for studying popularization of mathematics.</p>
<p style="margin-bottom: 0;">Speaker: Mr. Jeremy Porter (M.Sc.) </p>
<p style="margin-top:0;margin-bottom:0;">Date: Thursday, September 3, 2009</p>
<p style="margin-top:0;margin-bottom:0;">Time: 11:00 a.m.</p>
<p style="margin-top:0;margin-bottom:0;">Room: LB 921-4 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) </p>
<p style="margin-top:0;margin-bottom:0;">Title: On a Conjecture for the Distributions of Primes Associated with Elliptic Curves</p>
<p style="text-align:justify;margin-top:0;margin-bottom:0;">Abstract:   For an elliptic curve E and fixed integer r, Lang and Trotter have conjectured an asymptotic estimate for the number of primes p bounded by x such that the trace of Frobenius equals r. Using similar heuristic reasoning, Koblitz has conjectuerd an asymptotic estimate for the number of primes p bounded by x such that the order of the group of points of E over the finite field of prime characteristic p is also prime. These estimates have been proven correct for elliptic curves &ldquo;on average&rdquo;; however, beyond this the conjectures both remain open.</p>
<p style="text-align:justify; margin-top:0;">In this thesis, we combine the condition of Lang and Trotter with that of Koblitz to conjecture an asymptotic for the number of primes p bounded by x such that both the order of the group of points of E over the finite field of characteristic p is prime, and the trace of Frobenius equals r. In the case where E is a Serre curve, we will give an explicit construction for the estimate. As support for the conjecture, we will also provide several examples of Serre curves for which we computed the number of primes p bounded by large x such that the order of the group of points of E over the finite field of characteristic p is prime and the trace of Frobenius equals r, and compared this count with the conjectured estimates.</p>
<p style="margin-bottom: 0;">Speaker: Ms. Valerie Hudon (Ph.D.) </p>
<p style="margin-top:0;margin-bottom:0;">Date: Friday, August 28, 2009</p>
<p style="margin-top:0;margin-bottom:0;">Time: 10:30  a.m.</p>
<p style="margin-top:0;margin-bottom:0;">Room: AD 324 (Concordia University, Administration Building, 7141 Sherbrooke Street W.) </p>
<p style="margin-top:0;margin-bottom:0;">Title: Study of the Coadjoint Orbits of the Pointcare Group in 2 + 1 Dimensions and Theiry Coherent States</p>
<p style="text-align:justify; margin-top:0;">Abstract:  The first main objective of this thesis is to study the orbit structure of the (2+1)-Poincar&eacute; group (the symmetry group of relativity in two space and one time dimensions) by obtaining an explicit expression for the coadjoint  action.  From there, we compute and classify the coadjoint orbits.  We obtain a degenerate orbit, the upper and lower sheet of the two-sheet hyperboloid, the upper and lower cone and the one-sheet hyperboloid.  They appear as two-dimensional coadjoint orbits and, with their cotangent planes, as four-dimensional coadjoint orbits.  We also confirm a link between the four-dimensional coadjoint orbits and the orbits of the action of SO(2,1) on the dual of R^(2,1).<br />
    <br />
  The second main objective of this thesis is to use the information obtained about the structure to induce a representation and build the coherent states on two of the coadjoint orbits, namely the upper sheet of the two-sheet hyperboloid and the upper cone.  We obtain coherent states on the hyperboloid for the principal section.  The Galilean and the affine sections only allow us to get frames.  On the cone, we obtain a family of coherent states for a generalized principal section and a frame for the basic section.</p>
<p style="margin-bottom: 0;">Speaker: Mr. Baohua He (M.Sc.) </p>
<p style="margin-top:0;margin-bottom:0;">Date: Friday, August 21, 2009</p>
<p style="margin-top:0;margin-bottom:0;">Time: 2:00 p.m.</p>
<p style="margin-top:0;margin-bottom:0;">Room: LB 921-4 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) </p>
<p style="margin-top:0;margin-bottom:0;">Title: Smoothing Parameter Selection for a New Regression Estimator for Non-Negative Data</p>
<p style="text-align:justify; margin-top:0;">Abstract:   In this thesis, cross-validation based smoothing parameter election technique is applied to Chaubey, Laib and Sen&rsquo;s (2008) estimator, which is a new regression estimation for nonnegative random variables. The estimator is based on a generalization of Hille's lemma and a perturbation idea. A second order expansion for mean squared error (MSE) of the estimator is derived and the theoretical optimal values of the smoothing parameters are discussed and calculated. Simulation results and graphical illustrations on the new estimator comparing with Fan's (1992, 2003) local linear regression estimators are provided.</p>
<p style="margin-bottom: 0;">Speaker:  Ms. Tamanna Howlader (Ph.D.) </p>
<p style="margin-top:0;margin-bottom:0;">Date: Friday, June 19, 2009</p>
<p style="margin-top:0;margin-bottom:0;">Time: 1:30 p.m.</p>
<p style="margin-top:0;margin-bottom:0;">Room: LB 921-4 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) </p>
<p style="margin-top:0;margin-bottom:0;">Title: Wavelet-Based Noise Reduction of CDNA Microarray Images</p>
<p align="justify" style="margin-top:0;">Abstract:  Microarray experiments have greatly advanced our understanding of how genes function by enabling us to examine the activity of thousands of genes simultaneously. In cDNA microarray experiments, information regarding gene activity is extracted from a pair of red and green channel images. These images are often of poor quality since they are corrupted with noise arising from different sources, including the imaging system itself. Inferences based on noisy microarray images can be highly misleading. Many noise reduction algorithms have been proposed for natural images. Among these various methods, those that have been developed in the wavelet transform domain are found to be most successful. Unfortunately, the existing wavelet-based methods are not very efficient for reducing noise in cDNA microarray images because they are only capable of processing the red and green channel images separately. In doing so, they ignore the correlation that exists between the wavelet coefficients of the images in the two channels. This thesis deals with the problem of developing novel wavelet-based methods for reducing noise in cDNA microarray images for the purpose of obtaining accurate information regarding gene activity. Two types of wavelet transforms have been used. The proposed methods use joint statistical models that take into account the inter-channel dependencies for estimation of the noise-free images of the two channels. The performance of the proposed methods is compared with that of other methods through extensive experimentations which are carried out on a large set of microarray images. Results show that the new methods lead to improved noise reduction performance and more accurate estimation of the level of gene activity.  Thus, it is expected that these methods will play a significant role in improving the reliability of results obtained from real microarray images. </p>
<p style="margin-bottom: 0;">Speaker: Ms. Yuliya Klochko (Ph.D.)</p>
<p style="margin-top:0;margin-bottom:0;">Date: Monday, May 4, 2009</p>
<p style="margin-top:0;margin-bottom:0;">Time: 9:30 a.m.</p>
<p style="margin-top:0;margin-bottom:0;">Room: LB 646 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) </p>
<p style="margin-top:0;margin-bottom:0;">Title: Genus One Polyhedral Surfaces, Spaces of Quadratic Differentials On Tori and Determinants of Laplacians</p>
<p style="text-align:justify; margin-top:0;">Abstract:  This thesis presents a formula for the determinant of the Laplacian on an arbitrary compact polyhedral surface of genus one. The formula generalizes the well-known Ray-Singer result for a flat torus. A special case of flat conical metrics given by the modulus of a meromorphic quadratic differential on an elliptic curve is also considered. We study the determinant of the Laplacian as a functional on the moduli space of meromorphic quadratic differentials with L simple poles and L simple zeroes and derive formulas form variations of this functional with respect to natural coordinates on this space. We also give a new proof of Troyanov's theorem stating the existence of a conformal flat conical metric on a compact Riemann surface of arbitrary genus with a prescribed divisor of conical points.</p>
<p style="margin-bottom: 0;">Speaker: Ms. Olga Veres (Ph.D.)</p>
<p style="margin-top:0;margin-bottom:0;">Date: Wednesday, April 8, 2009</p>
<p style="margin-top:0;margin-bottom:0;">Time: 12:15 p.m.</p>
<p style="margin-top:0;margin-bottom:0;">Room: H 771 (Concordia University, Hall Building, 1455 de Maisonneuve Blvd. W.)</p>
<p style="margin-top:0;margin-bottom:0;">Title: On the Complexity of Polynomial Factorization Over P-adic Fields</p>
<p style="text-align:justify; margin-top:0;">Abstract:  Let p be a rational prime and &Phi; (x) be a monic irreducible polynomial in Zp[x]. Based on the work of Ore on Newton polygons (Ore, 1928) and MacLane's characterization of polynomial valuations (MacLane, 1936), Montes described an algorithm for the decomposition of the ideal pOK over an algebraic number field (Montes, 1999).  We give a simplified version of the Montes algorithm with a full Maple implementation which tests the irreducibility of &Phi; (x) over Qp. We derive an estimate of the complexity of this simplified algorithm in the worst case, when &Phi; (x) is irreducible over Qp. We show that in this case the algorithm terminates in at most O((deg &Phi;)^3+-epsilon v_p(disc &Phi;)^2+\epsilon) bit operations.  Lastly, we compare the "one-element" and "two-element" variations of the Zassenhaus "Round Four" algorithm with the Montes algorithm. </p>
<p style="margin-bottom: 0;">Speaker: Ms. Nadia Hardy (Ph.D.)</p>
<p style="margin-top:0;margin-bottom:0;">Date: Friday, April 3, 2009</p>
<p style="margin-top:0;margin-bottom:0;">Time: 2:30 p.m.</p>
<p style="margin-top:0;margin-bottom:0;">Room: LB 921-4 (Concordia University, Library Building, 1400 de Maisonneuve Blvd. W.) </p>
<p style="margin-top:0;margin-bottom:0;">Title: Students&rsquo; Models of the Knowledge to be Learned About Limits in College Level Calculus Courses.  The Influence of Routine Tasks and the Role Played By Institutional Norms</p>
<p style="text-align:justify; margin-top:0;">Abstract:  This thesis presents a study of instructors' and students' perceptions of the knowledge to be learned about limits of functions in a college level Calculus course, taught in a North American college institution. I have analyzed these perceptions from an anthropological perspective combining elements of the Anthropological Theory of Didactics, developed in mathematics education, with a framework for the study of institutions - the Institutional Analysis and Development framework - developed in political science. The analysis of these perceptions is based on empirical data: final examinations from the past six years (2001-2007), used in the studied College institution, and specially designed interviews with 28 students. While a model of the instructors' perceptions could be formulated mostly in mathematical terms,<br />
    <br />
  a model of the students' perceptions had to include an eclectic mixture of mathematical, social, cognitive and didactic norms. The analysis that I carry out shows that these students' perceptions have their source in the institutional emphasis on routine tasks and on the norms that regulate the institutional practices. Finally, I describe students' thinking about various tasks on limits from the perspective of Vygotsky's theory of concept development. Based on the 28 interviews that I have carried out, I will discuss the role of institutional practices on students' conceptual development.</p>
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